To take the bypass out of the loop temporarily, I think you'll need to join 2 of the 3 lines and cap the 3rd. If you use Sharkbite type press-on fittings, using their tool, you should be able to remove the new fittings when you get the new valve assembly.
One potential problem is that if you have braided line to the bypass valve, press-on fittings may need plastic inserts to add support to the walls of the tubing. If PEX, it'll be easier.
When you cut the current tubing, stay close to the valve so you don't have a fit problem attaching to the new valve assembly.
To figure out which 2 to join, you'll need to trace the plumbing from the city water inlet to the valve, and from the valve to the water heater cold input fitting.